AI 中文总结
研究在动态数据驱动应用系统中，利用多项式混沌展开提出新的非线性连续-离散跟踪滤波器（CD-PCE-CF），通过伽辽金投影推导系数预测和更新步骤，案例研究表明其在跟踪弹道物体时比CD-EKF在精度和稳定性上更优。
AI 中文摘要
在动态数据驱动应用系统（DDDAS）中，已提出非线性连续-离散（CD）跟踪算法，用于利用非线性离散时间测量序列递归估计遵循连续时间随机微分方程（SDE）的随机过程。本文提出了一种基于多项式混沌展开（PCE）的此类新滤波器作为这些跟踪问题的替代解决方案。利用PCE基的正交性，通过伽辽金投影推导PCE系数预测和更新步骤。这与以前基于PCE的滤波器不同，以前的滤波器在运动模型中独立传播配置点并在每个时间步重新计算PCE。因此，我们将所提出的滤波器称为CD-PCE系数滤波器（CD-PCE-CF）。提供了一个案例研究，其中使用CD-PCE-CF和CD扩展卡尔曼滤波器（CD-EKF）通过雷达测量跟踪受过程噪声影响的弹道物体。结果表明，所提出的方法在估计精度和稳定性方面明显优于CD-EKF。
英文摘要
In Dynamic Data Driven Applications Systems (DDDAS), non-linear continuous-discrete (CD) tracking algorithms have been proposed to recursively estimate stochastic processes which follow continuous-time stochastic differential equations (SDE) using non-linear discrete-time measurement sequences. In this paper, a new filter in this class which is based on the polynomial chaos expansion (PCE) is proposed as an alternative solution to these tracking problems. Using the orthogonality properties of the PCE basis, PCE coefficient-wise prediction and update steps are derived via the Galerkin projection. This differs from previous PCE based filters where collocation points are independently propagated through the motion model and the PCE is recomputed at each time step. For this reason, we call the proposed filter the CD-PCE coefficient filter (CD-PCE-CF). A case study is provided where the CD-PCE-CF and the CD-Extended Kalman Filter (CD-EKF) are used to track a ballistic object undergoing process noise using radar measurements. It is shown that the proposed method significantly outperforms the CD-EKF in terms of estimation accuracy and stability.
Comments8 pages, 2 figures, submitted to the 6th International Conference on Dynamic Data Driven Applications Systems (DDDAS 2026)
